Results and Spatial Analysis

Code
library(tidyverse)
library(sf)
library(tidycensus)
library(tigris)
library(spdep)
library(INLA)
library(BMA)
library(leaflet)
library(plotly)
library(dplyr)
library(DT)
library(kableExtra)
library(corrplot)
library(car)
library(viridis)
library(patchwork)
library(ggtext)
library(tidyr)
library(ggplot2)



# Set global options
options(tigris_use_cache = TRUE)
sf_use_s2(FALSE)

knitr::opts_chunk$set(
  echo = TRUE,
  message = FALSE,
  warning = FALSE,
  fig.align = "center",
  cache = TRUE
)

1 Empirical Results: Capability Deprivations

This chapter presents the main results from the INLA-BYM2 spatial analysis.

  • A one-unit increase in the DIESELPM (Environmental) is associated with approximately a 494.7% increase in the correctional population
  • Census Response: -73.6 Strong negative relationship ➡️ Suggests community engagement & collective efficacy matters!
  • Automobile access: -91
  • Homeownership: -40.8
  • Bachelor’s Degree: -88.4, Significant spatial clustering
  • Education-employment interaction

Credible Intervals:

- 95% probability that the true parameter lies within a specific range, given the data
- Not significant: Not statistically significant (CI crosses zero). Very small effect size

Key Effects on Supervision Rates

  • Environmental conditions (+494.7%)
  • Transportation barriers (-91.0%)
  • Educational access (-88.4%)
  • Healthcare availability (-73.3%)

Interpretation

  • Place strongly shapes outcomes
  • Multiple barriers compound
  • Resources matter significantly
  • Context affects success

2 Targeted Strategies: High-Risk Areas (Negative ui)

  1. Resource Development
    • Expand treatment options
    • Increase job programs
    • Improve transportation
    • Build support systems
  1. Barrier Reduction
    • Address access issues
    • Enhance coordination
    • Develop infrastructure
    • Strengthen networks

3 Relative Risk: Results Visualization and Policy Translation

Spatial Patterns: Relative Risk Mapping

3.0.1 Relative Risk: Air Pollution

Relative Risk values > 1, this means there is higher risk than expected. Areas with higher RR values likely have more Diesel Particulate Matter than expected. 2.42 in Carbon County, then there is 142% more correctional population than expected. Or a place like Morgan county is 0.21 RR has 79% lower correctional population than expected which likely represents an area with better air quality.

Map Interpretation
  • Red areas: Higher than expected correctional supervision rates (RR > 1.5)
  • Yellow areas: Near expected rates (RR 0.8-1.2)
  • Light areas: Lower than expected rates (RR < 0.8)
  • Pattern significance: Spatial clustering suggests collective capabilities matter

“Areas with poor air quality show 147% higher correctional supervision rates, suggesting environmental conditions may be an important upstream factor in justice system involvement” * Census tracts with poor air quality have 2.42 times higher risk of elevated correctional populations * For areas with similar characteristics but better air quality, this tract shows 147% higher correctional supervision rates * Air quality appears to be a significant environmental risk factor associated with correctional supervision rates

Potential Pathway: Poor Air Quality → Health Issues → Economic Stress → Community Instability → Higher Supervision Rates

Contributing Factors: 1. Health impacts affect employment 2. Medical costs create financial strain 3. Environmental stress on communities 4. Reduced outdoor activities/community engagement

3.1 Key Findings: Environmental Justice and Capabilities

3.1.1 Primary Finding: Air Pollution Impact

Major Discovery:

  • A one standard deviation increase in diesel particulate matter is associated with a 494.7% increase in correctional supervision rates, even after controlling for poverty, demographics, and other factors.

Capabilities Interpretation:

Air pollution serves as a powerful environmental conversion factor that constrains capability formation through:

  • Health impacts affecting employment stability
  • Environmental stress reducing community cohesion
  • Disproportionate burden on low-income communities
  • Compound effects with other environmental hazards

4 Environmental Conditions as Conversion Factors

4.1 Relative Risk: Air Quality Impact on Supervision

  • Relative Risk (RR) becomes a measure of capability deprivation in space. Combines fixed and random effects. Accounts for spatial structure.
exp(α + Σβjxij + ui + vi)
  • RR > 1, this means there is higher risk than expected. Areas with higher RR values likely have more Diesel Particulate Matter than expected. High RR clusters → capability deprivation (RR = 1: Expected risk level. RR < 1: Lower risk than expected)

  • 2.42 in Carbon County, then there is 142% more correctional population than expected. Or a place like Morgan county is 0.21 RR has 79% lower correctional population than expected which likely represents an area with better air quality.

4.1.0.1 Pathway to Supervision

  1. Direct Health Effects
    • Increased stress
    • Physical health impacts
    • Mental health strain
    • Cognitive effects
  2. Economic Impact
    • Healthcare costs
    • Work disruption
    • Medical expenses
    • Employment stability
  3. Social Consequences
    • Reduced outdoor activity
    • Limited community engagement
    • Restricted social networks
    • Decreased collective efficacy

4.2 Geographic Distribution

4.2.1 Clustering Effects

  • Environmental hazards concentrate spatially
  • Poor air quality clusters with other disadvantages
  • Health impacts compound over time
  • Community capabilities constrained

4.2.2 Relative Risk Interpretation

  • RR > 2.0: Severe capability constraint
  • RR 1.5-2.0: Moderate impact
  • RR < 1.0: Better environmental conditions “Areas with poor air quality show 147% higher correctional supervision rates, suggesting environmental conditions may be an important upstream factor in justice system involvement”
  • Census tracts with poor air quality have 2.42 times higher risk of elevated correctional populations
  • For areas with similar characteristics but better air quality, this tract shows 147% higher correctional supervision rates
  • Air quality appears to be a significant environmental risk factor associated with correctional supervision rates

Potential Pathway: Poor Air Quality → Health Issues → Economic Stress → Community Instability → Higher Supervision Rates

Contributing Factors: 1. Health impacts affect employment 2. Medical costs create financial strain 3. Environmental stress on communities 4. Reduced outdoor activities/community engagement

5 Statistical Results

6 Spatial Components

Code
spatial_components <- data.frame(
  Component = c("Structured (Phi)", "Precision (re_u)", "Precision (re_v)"),
  Value = c(0.594, 2.79, 21100),
  Interpretation = c("59.4% spatial structure",
                    "Strong spatial dependence",
                    "Low unstructured variation")
)

DT::datatable(spatial_components,
              options = list(pageLength = 5),
              rownames = FALSE)

6.0.1 Protective Factors: Access and Engagement

Code
protective_data <- data.frame(
  Factor = c("Census Response\n(Community Engagement)", 
             "Automobile Access\n(Transportation)", 
             "Health Insurance\n(Healthcare Access)",
             "Employment Rate\n(Economic Opportunity)"),
  Risk_Reduction = c(73.6, 91.0, 72.6, 50.0),
  Theory_Connection = c("Collective Efficacy", "Mobility Access", "Health Security", "Economic Stability")
)

ggplot(protective_data, aes(x = reorder(Factor, Risk_Reduction), y = Risk_Reduction, 
                           fill = Theory_Connection)) +
  geom_col(alpha = 0.8) +
  geom_text(aes(label = paste0("-", Risk_Reduction, "%")), 
            hjust = -0.1, size = 4, fontface = "bold") +
  coord_flip() +
  scale_fill_viridis_d(option = "plasma", alpha = 0.8) +
  labs(x = "Conversion Factor", 
       y = "Risk Reduction (%)",
       title = "Protective Conversion Factors",
       subtitle = "How access and engagement reduce correctional supervision risk",
       fill = "Theoretical Domain") +
  theme_minimal() +
  theme(text = element_text(size = 12))

6.0.2 Implementation Focus

  • Target highest-need areas
  • Address multiple barriers
  • Build community capacity
  • Enhance coordination